angle — Phase angle (argument) of real and complex values in MATLAB and RunMat.

angle(x) returns the phase angle (argument) of each element in x, in radians. Complex inputs use atan2(imag(x), real(x)), and real-valued arrays are handled element-wise with MATLAB/RunMat-compatible results.

Syntax

theta = angle(X)

Inputs

Returns

Errors

How angle works

• Complex inputs use atan2(imag(x), real(x)), yielding values in [-π, π].
• Real inputs are treated as complex numbers with zero imaginary part. Positive numbers map to 0, negative numbers map to π, and zeros return 0.
• Logical inputs are promoted to doubles (true → 1, false → 0) before computing the angle.
• Results are always returned as dense double-precision arrays that preserve the shape of the input.
• Character arrays are interpreted as their numeric code points and produce double arrays of the same size.
• String arrays are unsupported and raise an error, mirroring MATLAB.
• NaN propagation follows IEEE rules: angle(NaN) returns NaN.

Does RunMat run angle on the GPU?

When RunMat Accelerate is active, tensors that already reside on the GPU remain on the device. Providers that implement the unary_angle hook execute the phase computation directly on the GPU, using atan2(0, real) for real storage and atan2(imag, real) for complex-interleaved storage. If the hook is missing or an input requires host-only conversion, RunMat gathers the data, evaluates the phase angle on the CPU, and then honors any downstream fusion or residency decisions automatically.

GPU memory and residency

You usually do not need to call gpuArray explicitly. RunMat's fusion planner and Accelerate layer manage residency automatically, keeping tensors on the GPU whenever device execution is advantageous. Explicit gpuArray / gather calls remain available for MATLAB compatibility or when you need deterministic residency control.

Examples

Computing the phase of a complex scalar

z = 3 + 4i;
theta = angle(z);
disp(theta)

Expected output:

theta = 0.9273

Extracting angles from a complex vector

Z = [1+1i, -1+1i, -1-1i, 1-1i];
phases = angle(Z);
disp(phases)

Expected output:

phases = [0.7854 2.3562 -2.3562 -0.7854]

Determining angles of negative real numbers

vals = [-2 -1 0 1 2];
phi = angle(vals);
disp(phi)

Expected output:

phi = [3.1416 3.1416 0 0 0]

Working with GPU-resident arrays

G = gpuArray([1 -1; -1 1]);
theta = gather(angle(G));
disp(theta)

Expected output:

theta =

     0.0000    3.1416
     3.1416    0.0000

Angles of character code arrays

C = ['A' 'B'; 'C' 'D'];
codes = angle(C);
disp(codes)

Expected output:

codes = [0 0; 0 0]

Angles from logical masks

mask = logical([0 1; 1 0]);
phaseMask = angle(mask);
disp(phaseMask)

Expected output:

phaseMask = [0 0; 0 0]

Using angle with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how angle changes the result.

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how angle is executed, line by line, in Rust.

• View the source for angle in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

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